Exact solution for the Lindbladian dynamics for the open XX spin chain with boundary dissipation

We obtain exact formulas for the time-dependence of a few physical observables open XX spin chain with Lindbladian dynamics. Our analysis is based on fact that Lindblad equation an arbitrary quadratic system N N fermions explicitly solved in terms diagonalization 4N\times4N display="inline">4N×4N matrix called structure by following scheme third quantization. mainly focus magnetization and current. As short-time behavior at given site, we observe plateau regime except near center chain. Basic features this are explained light-cone created propagations boundary effects from initial time, but can explain their more detailed properties analytically using our formulas. On other hand, after regime, current exhibit slow decay to steady state values described Liouvillian gap. establish its O(N^{-3}) display="inline">O(N−3) scaling also determine coefficient.